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arXiv · 2512.22960

Standing waves of the Anderson-Gross-Pitaevskii equation

Samaël Mackowiak
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Abstract

In this paper, we study standing waves for the Anderson-Gross-Pitaevskii equation in dimension 1 and 2. The Anderson-Gross-Pitaevskii equation is a nonlinear Schr\"odinger equation with a confining potential and a multiplicative spatial white noise. Standing waves are characterized by a profile which is invariant by the dynamic and solves a nonlinear elliptic equation with spatial white noise potential. We construct such solutions via variational methods and obtain some results on their regularity, localization and stability.

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Samaël Mackowiak. 2025-12-28. Standing waves of the Anderson-Gross-Pitaevskii equation. https://arxiv.org/abs/2512.22960

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